The gravity of modern amplitudes: using on-shell scattering amplitudes to probe gravity
In this thesis, we explore the use of on-shell scattering amplitudes as a way to understand various gravitational phenomena. We show that amplitudes are a viable way of studying certain aspects of gravity and showcase three such novel results here. First is the computation of the deflection angle of both light and gravitational waves due to a massive static body. We compute this from a purely on-shell amplitude perspective and find that the result is in complete agreement with the corresponding calculation in General Relativity. The second is the ability to derive classical results from the amplitudes. In this section we use on-shell scattering amplitudes to derive the perturbative metric of a rotating black hole in a generic form of Einstein gravity that has additional terms cubic in the Riemann tensor. We show that the metric we derive reduces to correct static metric in the zero angular momentum limit. We show that at first order in the coupling, the classical potential can be written to all orders in spin as a differential operator acting on the non-rotating potential. Further we compute the classical impulse and scattering angle of such a black hole. The third is the resolution of a classical discontinuity in N = 1 super gravity. Here we use on-shell methods for massive particles and use them to compute the supersymmetric version of the van Damme-Veltman-Zakharov (vDVZ) discontinuity. We construct the amplitudes of massive gravitinos (the superpartner of massive gravitons) and show that in the massless limit of the gravitinos there is the same discontinuity as found in massive gravity. This method sheds light on intricacies of the discontinuity that is obscured when handled classically.
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Department of Mathematics and Applied Mathematics